Université Paris 6
Pierre et Marie Curie
Université Paris 7
Denis Diderot

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

Error analysis of the quantization algorithm for obstacle problems


Code(s) de Classification MSC:

Résumé: In the accompanying paper [2] an algorithm based on a "quantized tree" is designed to compute the solution of multi-dimensional obstacle problems for homogeneous $\RR^d$-valued Markov chains. It is based on the quantization of probability distributions which yields a dynamic programming formula on a discrete tree. A typical example of such problems is the pricing of multi-asset American style vanilla options. In the first part of the present paper, the analysis of the $L^p$-error is completed. In the second part, we estimate the error induced by the Monte Carlo estimation of the transition weights involved in the (optimal) quantized tree.

Mots Clés: Numerical Probability ; Optimal Stopping ; Snell envelope ; Quantization of random variables ; Reflected Backward Stochastic Differential Equation ; American option pricing

Date: 2001-03-08

Prépublication numéro: PMA-642